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<div class="subTitle">org.apache.commons.math3.ode.nonstiff</div>
<h2 title="Class AdamsMoultonIntegrator" class="title">Class AdamsMoultonIntegrator</h2>
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<li><a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">org.apache.commons.math3.ode.AbstractIntegrator</a></li>
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<li><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator</a></li>
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<li><a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html" title="class in org.apache.commons.math3.ode">org.apache.commons.math3.ode.MultistepIntegrator</a></li>
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<li><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">org.apache.commons.math3.ode.nonstiff.AdamsIntegrator</a></li>
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<li>org.apache.commons.math3.ode.nonstiff.AdamsMoultonIntegrator</li>
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<dt>All Implemented Interfaces:</dt>
<dd><a href="../../../../../../org/apache/commons/math3/ode/FirstOrderIntegrator.html" title="interface in org.apache.commons.math3.ode">FirstOrderIntegrator</a>, <a href="../../../../../../org/apache/commons/math3/ode/ODEIntegrator.html" title="interface in org.apache.commons.math3.ode">ODEIntegrator</a></dd>
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<pre>public class <span class="strong">AdamsMoultonIntegrator</span>
extends <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdamsIntegrator</a></pre>
<div class="block">This class implements implicit Adams-Moulton integrators for Ordinary
 Differential Equations.

 <p>Adams-Moulton methods (in fact due to Adams alone) are implicit
 multistep ODE solvers. This implementation is a variation of the classical
 one: it uses adaptive stepsize to implement error control, whereas
 classical implementations are fixed step size. The value of state vector
 at step n+1 is a simple combination of the value at step n and of the
 derivatives at steps n+1, n, n-1 ... Since y'<sub>n+1</sub> is needed to
 compute y<sub>n+1</sub>, another method must be used to compute a first
 estimate of y<sub>n+1</sub>, then compute y'<sub>n+1</sub>, then compute
 a final estimate of y<sub>n+1</sub> using the following formulas. Depending
 on the number k of previous steps one wants to use for computing the next
 value, different formulas are available for the final estimate:</p>
 <ul>
   <li>k = 1: y<sub>n+1</sub> = y<sub>n</sub> + h y'<sub>n+1</sub></li>
   <li>k = 2: y<sub>n+1</sub> = y<sub>n</sub> + h (y'<sub>n+1</sub>+y'<sub>n</sub>)/2</li>
   <li>k = 3: y<sub>n+1</sub> = y<sub>n</sub> + h (5y'<sub>n+1</sub>+8y'<sub>n</sub>-y'<sub>n-1</sub>)/12</li>
   <li>k = 4: y<sub>n+1</sub> = y<sub>n</sub> + h (9y'<sub>n+1</sub>+19y'<sub>n</sub>-5y'<sub>n-1</sub>+y'<sub>n-2</sub>)/24</li>
   <li>...</li>
 </ul>

 <p>A k-steps Adams-Moulton method is of order k+1.</p>

 <h3>Implementation details</h3>

 <p>We define scaled derivatives s<sub>i</sub>(n) at step n as:
 <pre>
 s<sub>1</sub>(n) = h y'<sub>n</sub> for first derivative
 s<sub>2</sub>(n) = h<sup>2</sup>/2 y''<sub>n</sub> for second derivative
 s<sub>3</sub>(n) = h<sup>3</sup>/6 y'''<sub>n</sub> for third derivative
 ...
 s<sub>k</sub>(n) = h<sup>k</sup>/k! y<sup>(k)</sup><sub>n</sub> for k<sup>th</sup> derivative
 </pre></p>

 <p>The definitions above use the classical representation with several previous first
 derivatives. Lets define
 <pre>
   q<sub>n</sub> = [ s<sub>1</sub>(n-1) s<sub>1</sub>(n-2) ... s<sub>1</sub>(n-(k-1)) ]<sup>T</sup>
 </pre>
 (we omit the k index in the notation for clarity). With these definitions,
 Adams-Moulton methods can be written:
 <ul>
   <li>k = 1: y<sub>n+1</sub> = y<sub>n</sub> + s<sub>1</sub>(n+1)</li>
   <li>k = 2: y<sub>n+1</sub> = y<sub>n</sub> + 1/2 s<sub>1</sub>(n+1) + [ 1/2 ] q<sub>n+1</sub></li>
   <li>k = 3: y<sub>n+1</sub> = y<sub>n</sub> + 5/12 s<sub>1</sub>(n+1) + [ 8/12 -1/12 ] q<sub>n+1</sub></li>
   <li>k = 4: y<sub>n+1</sub> = y<sub>n</sub> + 9/24 s<sub>1</sub>(n+1) + [ 19/24 -5/24 1/24 ] q<sub>n+1</sub></li>
   <li>...</li>
 </ul></p>

 <p>Instead of using the classical representation with first derivatives only (y<sub>n</sub>,
 s<sub>1</sub>(n+1) and q<sub>n+1</sub>), our implementation uses the Nordsieck vector with
 higher degrees scaled derivatives all taken at the same step (y<sub>n</sub>, s<sub>1</sub>(n)
 and r<sub>n</sub>) where r<sub>n</sub> is defined as:
 <pre>
 r<sub>n</sub> = [ s<sub>2</sub>(n), s<sub>3</sub>(n) ... s<sub>k</sub>(n) ]<sup>T</sup>
 </pre>
 (here again we omit the k index in the notation for clarity)
 </p>

 <p>Taylor series formulas show that for any index offset i, s<sub>1</sub>(n-i) can be
 computed from s<sub>1</sub>(n), s<sub>2</sub>(n) ... s<sub>k</sub>(n), the formula being exact
 for degree k polynomials.
 <pre>
 s<sub>1</sub>(n-i) = s<sub>1</sub>(n) + &sum;<sub>j&gt;0</sub> (j+1) (-i)<sup>j</sup> s<sub>j+1</sub>(n)
 </pre>
 The previous formula can be used with several values for i to compute the transform between
 classical representation and Nordsieck vector. The transform between r<sub>n</sub>
 and q<sub>n</sub> resulting from the Taylor series formulas above is:
 <pre>
 q<sub>n</sub> = s<sub>1</sub>(n) u + P r<sub>n</sub>
 </pre>
 where u is the [ 1 1 ... 1 ]<sup>T</sup> vector and P is the (k-1)&times;(k-1) matrix built
 with the (j+1) (-i)<sup>j</sup> terms with i being the row number starting from 1 and j being
 the column number starting from 1:
 <pre>
        [  -2   3   -4    5  ... ]
        [  -4  12  -32   80  ... ]
   P =  [  -6  27 -108  405  ... ]
        [  -8  48 -256 1280  ... ]
        [          ...           ]
 </pre></p>

 <p>Using the Nordsieck vector has several advantages:
 <ul>
   <li>it greatly simplifies step interpolation as the interpolator mainly applies
   Taylor series formulas,</li>
   <li>it simplifies step changes that occur when discrete events that truncate
   the step are triggered,</li>
   <li>it allows to extend the methods in order to support adaptive stepsize.</li>
 </ul></p>

 <p>The predicted Nordsieck vector at step n+1 is computed from the Nordsieck vector at step
 n as follows:
 <ul>
   <li>Y<sub>n+1</sub> = y<sub>n</sub> + s<sub>1</sub>(n) + u<sup>T</sup> r<sub>n</sub></li>
   <li>S<sub>1</sub>(n+1) = h f(t<sub>n+1</sub>, Y<sub>n+1</sub>)</li>
   <li>R<sub>n+1</sub> = (s<sub>1</sub>(n) - S<sub>1</sub>(n+1)) P<sup>-1</sup> u + P<sup>-1</sup> A P r<sub>n</sub></li>
 </ul>
 where A is a rows shifting matrix (the lower left part is an identity matrix):
 <pre>
        [ 0 0   ...  0 0 | 0 ]
        [ ---------------+---]
        [ 1 0   ...  0 0 | 0 ]
    A = [ 0 1   ...  0 0 | 0 ]
        [       ...      | 0 ]
        [ 0 0   ...  1 0 | 0 ]
        [ 0 0   ...  0 1 | 0 ]
 </pre>
 From this predicted vector, the corrected vector is computed as follows:
 <ul>
   <li>y<sub>n+1</sub> = y<sub>n</sub> + S<sub>1</sub>(n+1) + [ -1 +1 -1 +1 ... &plusmn;1 ] r<sub>n+1</sub></li>
   <li>s<sub>1</sub>(n+1) = h f(t<sub>n+1</sub>, y<sub>n+1</sub>)</li>
   <li>r<sub>n+1</sub> = R<sub>n+1</sub> + (s<sub>1</sub>(n+1) - S<sub>1</sub>(n+1)) P<sup>-1</sup> u</li>
 </ul>
 where the upper case Y<sub>n+1</sub>, S<sub>1</sub>(n+1) and R<sub>n+1</sub> represent the
 predicted states whereas the lower case y<sub>n+1</sub>, s<sub>n+1</sub> and r<sub>n+1</sub>
 represent the corrected states.</p>

 <p>The P<sup>-1</sup>u vector and the P<sup>-1</sup> A P matrix do not depend on the state,
 they only depend on k and therefore are precomputed once for all.</p></div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>2.0</dd></dl>
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<h3>Nested classes/interfaces inherited from class&nbsp;org.apache.commons.math3.ode.<a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html" title="class in org.apache.commons.math3.ode">MultistepIntegrator</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.NordsieckTransformer.html" title="interface in org.apache.commons.math3.ode">MultistepIntegrator.NordsieckTransformer</a></code></li>
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<h3>Fields inherited from class&nbsp;org.apache.commons.math3.ode.<a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html" title="class in org.apache.commons.math3.ode">MultistepIntegrator</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#nordsieck">nordsieck</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#scaled">scaled</a></code></li>
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<h3>Fields inherited from class&nbsp;org.apache.commons.math3.ode.nonstiff.<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdaptiveStepsizeIntegrator</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#mainSetDimension">mainSetDimension</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#scalAbsoluteTolerance">scalAbsoluteTolerance</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#scalRelativeTolerance">scalRelativeTolerance</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#vecAbsoluteTolerance">vecAbsoluteTolerance</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#vecRelativeTolerance">vecRelativeTolerance</a></code></li>
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<h3>Fields inherited from class&nbsp;org.apache.commons.math3.ode.<a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">AbstractIntegrator</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#isLastStep">isLastStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#resetOccurred">resetOccurred</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#stepHandlers">stepHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#stepSize">stepSize</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#stepStart">stepStart</a></code></li>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.html#AdamsMoultonIntegrator(int,%20double,%20double,%20double[],%20double[])">AdamsMoultonIntegrator</a></strong>(int&nbsp;nSteps,
                      double&nbsp;minStep,
                      double&nbsp;maxStep,
                      double[]&nbsp;vecAbsoluteTolerance,
                      double[]&nbsp;vecRelativeTolerance)</code>
<div class="block">Build an Adams-Moulton integrator with the given order and error control parameters.</div>
</td>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.html#AdamsMoultonIntegrator(int,%20double,%20double,%20double,%20double)">AdamsMoultonIntegrator</a></strong>(int&nbsp;nSteps,
                      double&nbsp;minStep,
                      double&nbsp;maxStep,
                      double&nbsp;scalAbsoluteTolerance,
                      double&nbsp;scalRelativeTolerance)</code>
<div class="block">Build an Adams-Moulton integrator with the given order and error control parameters.</div>
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<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.html#integrate(org.apache.commons.math3.ode.ExpandableStatefulODE,%20double)">integrate</a></strong>(<a href="../../../../../../org/apache/commons/math3/ode/ExpandableStatefulODE.html" title="class in org.apache.commons.math3.ode">ExpandableStatefulODE</a>&nbsp;equations,
         double&nbsp;t)</code>
<div class="block">Integrate a set of differential equations up to the given time.</div>
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<h3>Methods inherited from class&nbsp;org.apache.commons.math3.ode.nonstiff.<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdamsIntegrator</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html#initializeHighOrderDerivatives(double,%20double[],%20double[][],%20double[][])">initializeHighOrderDerivatives</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html#updateHighOrderDerivativesPhase1(org.apache.commons.math3.linear.Array2DRowRealMatrix)">updateHighOrderDerivativesPhase1</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html#updateHighOrderDerivativesPhase2(double[],%20double[],%20org.apache.commons.math3.linear.Array2DRowRealMatrix)">updateHighOrderDerivativesPhase2</a></code></li>
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<h3>Methods inherited from class&nbsp;org.apache.commons.math3.ode.<a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html" title="class in org.apache.commons.math3.ode">MultistepIntegrator</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#computeStepGrowShrinkFactor(double)">computeStepGrowShrinkFactor</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getMaxGrowth()">getMaxGrowth</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getMinReduction()">getMinReduction</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getNSteps()">getNSteps</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getSafety()">getSafety</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#getStarterIntegrator()">getStarterIntegrator</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#setMaxGrowth(double)">setMaxGrowth</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#setMinReduction(double)">setMinReduction</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#setSafety(double)">setSafety</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#setStarterIntegrator(org.apache.commons.math3.ode.FirstOrderIntegrator)">setStarterIntegrator</a>, <a href="../../../../../../org/apache/commons/math3/ode/MultistepIntegrator.html#start(double,%20double[],%20double)">start</a></code></li>
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<h3>Methods inherited from class&nbsp;org.apache.commons.math3.ode.nonstiff.<a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdaptiveStepsizeIntegrator</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#filterStep(double,%20boolean,%20boolean)">filterStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#getCurrentStepStart()">getCurrentStepStart</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#getMaxStep()">getMaxStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#getMinStep()">getMinStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#initializeStep(boolean,%20int,%20double[],%20double,%20double[],%20double[],%20double[],%20double[])">initializeStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#resetInternalState()">resetInternalState</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#sanityChecks(org.apache.commons.math3.ode.ExpandableStatefulODE,%20double)">sanityChecks</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#setInitialStepSize(double)">setInitialStepSize</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#setStepSizeControl(double,%20double,%20double[],%20double[])">setStepSizeControl</a>, <a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdaptiveStepsizeIntegrator.html#setStepSizeControl(double,%20double,%20double,%20double)">setStepSizeControl</a></code></li>
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<h3>Methods inherited from class&nbsp;org.apache.commons.math3.ode.<a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html" title="class in org.apache.commons.math3.ode">AbstractIntegrator</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#acceptStep(org.apache.commons.math3.ode.sampling.AbstractStepInterpolator,%20double[],%20double[],%20double)">acceptStep</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#addEventHandler(org.apache.commons.math3.ode.events.EventHandler,%20double,%20double,%20int)">addEventHandler</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#addEventHandler(org.apache.commons.math3.ode.events.EventHandler,%20double,%20double,%20int,%20org.apache.commons.math3.analysis.solvers.UnivariateSolver)">addEventHandler</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#addStepHandler(org.apache.commons.math3.ode.sampling.StepHandler)">addStepHandler</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#clearEventHandlers()">clearEventHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#clearStepHandlers()">clearStepHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#computeDerivatives(double,%20double[],%20double[])">computeDerivatives</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getCounter()">getCounter</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getCurrentSignedStepsize()">getCurrentSignedStepsize</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getEvaluations()">getEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getEvaluationsCounter()">getEvaluationsCounter</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getEventHandlers()">getEventHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getExpandable()">getExpandable</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getMaxEvaluations()">getMaxEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getName()">getName</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getStepHandlers()">getStepHandlers</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#initIntegration(double,%20double[],%20double)">initIntegration</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#integrate(org.apache.commons.math3.ode.FirstOrderDifferentialEquations,%20double,%20double[],%20double,%20double[])">integrate</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#setEquations(org.apache.commons.math3.ode.ExpandableStatefulODE)">setEquations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#setMaxEvaluations(int)">setMaxEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#setStateInitialized(boolean)">setStateInitialized</a></code></li>
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<h3>Methods inherited from class&nbsp;java.lang.<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long,%20int)" title="class or interface in java.lang">wait</a></code></li>
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<a name="AdamsMoultonIntegrator(int, double, double, double, double)">
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<h4>AdamsMoultonIntegrator</h4>
<pre>public&nbsp;AdamsMoultonIntegrator(int&nbsp;nSteps,
                      double&nbsp;minStep,
                      double&nbsp;maxStep,
                      double&nbsp;scalAbsoluteTolerance,
                      double&nbsp;scalRelativeTolerance)
                       throws <a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></pre>
<div class="block">Build an Adams-Moulton integrator with the given order and error control parameters.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>nSteps</code> - number of steps of the method excluding the one being computed</dd><dd><code>minStep</code> - minimal step (sign is irrelevant, regardless of
 integration direction, forward or backward), the last step can
 be smaller than this</dd><dd><code>maxStep</code> - maximal step (sign is irrelevant, regardless of
 integration direction, forward or backward), the last step can
 be smaller than this</dd><dd><code>scalAbsoluteTolerance</code> - allowed absolute error</dd><dd><code>scalRelativeTolerance</code> - allowed relative error</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if order is 1 or less</dd></dl>
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<h4>AdamsMoultonIntegrator</h4>
<pre>public&nbsp;AdamsMoultonIntegrator(int&nbsp;nSteps,
                      double&nbsp;minStep,
                      double&nbsp;maxStep,
                      double[]&nbsp;vecAbsoluteTolerance,
                      double[]&nbsp;vecRelativeTolerance)
                       throws <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></pre>
<div class="block">Build an Adams-Moulton integrator with the given order and error control parameters.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>nSteps</code> - number of steps of the method excluding the one being computed</dd><dd><code>minStep</code> - minimal step (sign is irrelevant, regardless of
 integration direction, forward or backward), the last step can
 be smaller than this</dd><dd><code>maxStep</code> - maximal step (sign is irrelevant, regardless of
 integration direction, forward or backward), the last step can
 be smaller than this</dd><dd><code>vecAbsoluteTolerance</code> - allowed absolute error</dd><dd><code>vecRelativeTolerance</code> - allowed relative error</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - if order is 1 or less</dd></dl>
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<h3>Method Detail</h3>
<a name="integrate(org.apache.commons.math3.ode.ExpandableStatefulODE, double)">
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<h4>integrate</h4>
<pre>public&nbsp;void&nbsp;integrate(<a href="../../../../../../org/apache/commons/math3/ode/ExpandableStatefulODE.html" title="class in org.apache.commons.math3.ode">ExpandableStatefulODE</a>&nbsp;equations,
             double&nbsp;t)
               throws <a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a>,
                      <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
                      <a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a>,
                      <a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></pre>
<div class="block">Integrate a set of differential equations up to the given time.
 <p>This method solves an Initial Value Problem (IVP).</p>
 <p>The set of differential equations is composed of a main set, which
 can be extended by some sets of secondary equations. The set of
 equations must be already set up with initial time and partial states.
 At integration completion, the final time and partial states will be
 available in the same object.</p>
 <p>Since this method stores some internal state variables made
 available in its public interface during integration (<a href="../../../../../../org/apache/commons/math3/ode/AbstractIntegrator.html#getCurrentSignedStepsize()"><code>AbstractIntegrator.getCurrentSignedStepsize()</code></a>), it is <em>not</em> thread-safe.</p></div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html#integrate(org.apache.commons.math3.ode.ExpandableStatefulODE,%20double)">integrate</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../../org/apache/commons/math3/ode/nonstiff/AdamsIntegrator.html" title="class in org.apache.commons.math3.ode.nonstiff">AdamsIntegrator</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>equations</code> - complete set of differential equations to integrate</dd><dd><code>t</code> - target time for the integration
 (can be set to a value smaller than <code>t0</code> for backward integration)</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if integration step is too small</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the dimension of the complete state does not
 match the complete equations sets dimension</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - if the number of functions evaluations is exceeded</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></code> - if the location of an event cannot be bracketed</dd></dl>
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